Hilbert schemes of skew lines on cubic threefolds

Abstract: On a smooth cubic threefold Y, a pairs of skew lines determines an irreducible component H of the Hilbert scheme of Y. We will show that the component H is smooth and is isomorphic to the blow-up of the 2nd symmetric product of Fano surface of lines on Y along the diagonal. This work is based on the work on Hilbert schemes of skew lines on projective spaces by Chen-Coskun-Nollet in 2011. Moreover, I'll explain the relation of the component H to the compactification of locus of vanishing cycles on hyperplane sections of Y and the stable moduli space considered by Altavilla-Petkovic-Rota.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic